The publication “Adaptive Cruise Control System Aspect and Development Trends” by Winner, Witte, Uhler and Lichtenberg, published at the SAE International Congress and Exposition, Detroit, Feb. 26–29, 1996 (SAE paper 961010), describes an adaptive cruise control which emits a radar beam and receives the portion of the beam reflected by stationary objects and preceding vehicles. If this cruise control recognizes a preceding vehicle, cruise control is performed as a constant distance regulation in relation to the preceding vehicle. If the radar system does not detect a preceding vehicle, cruise control is performed as a constant-speed regulation at a set speed defined by the driver. The accelerations and changes in acceleration over time implementable by adaptive cruise controls are limited here by fixed maximum values, because the adaptive cruise control is intended as a comfort system for driver support and therefore aims at a comfortable driving characteristic. The disadvantage of such systems in which the acceleration gradients are determined independently of the dynamic data of preceding vehicles is that these acceleration jolts cause discomfort. In non-critical situations, for example, when approaching a preceding vehicle at a low relative speed, the fixedly predefined acceleration jolt is perceived as too high and therefore uncomfortable, and in situations in which a collision is to be avoided, for example, when approaching a preceding vehicle at a high relative speed, the deceleration gradient is too low, so that driver intervention is generally necessary. In the context of the present invention, the term “acceleration” is used for both positive accelerations and negative accelerations, i.e., decelerations.